{
  "id": "1901.06267",
  "version": "v1",
  "published": "2019-01-15T10:07:52.000Z",
  "updated": "2019-01-15T10:07:52.000Z",
  "title": "Log-affine geodesics in the manifold of vector states on a von Neumann algebra",
  "authors": [
    "Jan Naudts"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "This paper introduces the notion of a log-affine geodesic connecting two vector states on a von Neumann algebra. The definition is linked to the standard notion of Boltzmann-Gibbs states in statistical physics and the related notion of quantum statistical manifolds. In the abelian case it is linked to the notion of exponential tangent spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T10:07:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "von neumann algebra",
      "vector states",
      "log-affine geodesic",
      "exponential tangent spaces",
      "abelian case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}